Problem: Solve for $x$ and $y$ using elimination. ${-2x-2y = -22}$ ${2x-5y = 15}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-7y = -7$ $\dfrac{-7y}{{-7}} = \dfrac{-7}{{-7}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-2x-2y = -22}\thinspace$ to find $x$ ${-2x - 2}{(1)}{= -22}$ $-2x-2 = -22$ $-2x-2{+2} = -22{+2}$ $-2x = -20$ $\dfrac{-2x}{{-2}} = \dfrac{-20}{{-2}}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {2x-5y = 15}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(1)}{= 15}$ ${x = 10}$